Hydrated calcium sulfate contains 55.8% sulfate by mass. Calculate the value for "n".
To calculate the value of "n" in hydrated calcium sulfate, we need to understand the chemical formula of hydrated calcium sulfate and the percentage composition of sulfate.
The chemical formula for hydrated calcium sulfate is typically written as CaSO₄·nH₂O, where "n" represents the number of water molecules associated with each calcium sulfate unit.
Given that hydrated calcium sulfate contains 55.8% sulfate by mass, we can calculate the molar ratio of sulfate in relation to calcium sulfate. To do this, we assume a 100g sample of the compound.
Since sulfate (SO₄²⁻) has a molar mass of 96 g/mol, we can determine the mass of sulfate in the sample by multiplying the percentage composition (55.8%) by the total mass of the sample (100g):
Mass of sulfate = 55.8% × 100g = 55.8g
Next, we convert the mass of sulfate to moles. The molar mass of sulfate (SO₄²⁻) is 96 g/mol, so:
Moles of sulfate = Mass of sulfate / Molar mass of sulfate = 55.8g / 96 g/mol ≈ 0.581 mol
Now, let's calculate the moles of calcium sulfate (CaSO₄). Since calcium sulfate has a molar mass of 136 g/mol, we can use the molar ratio between calcium sulfate and sulfate to find the number of moles of calcium sulfate:
Moles of calcium sulfate = Moles of sulfate × (1 mol calcium sulfate / 1 mol sulfate) = 0.581 mol
Finally, the value of "n" in the chemical formula CaSO₄·nH₂O represents the number of moles of water for each mole of calcium sulfate. The equation is balanced such that there is a 1:1 ratio between moles of calcium sulfate and moles of water. Therefore, "n" is equal to the moles of calcium sulfate.
Hence, in this case, "n" is approximately equal to 0.581.